Originally posted by: SystemAdmin

[ArushGadkar said:]

Hello All,
I have a variable binary vector lets say U[5]. I have a variable integer vector lets say S[5]. The constraint i am trying to formulate is as follows:

sum over all j ----> U[j]*S[j] <= C (some fixed integer) .<br />
Example if U[5] = [ 1, 1, 0 , 0, 1] then i want to formulate the constraint S[1] + S[2] + S[5] <= C.<br />
Your help is very much appreciated.
Thanks
Arush.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[voydge said:]

I think you can:

range Size=1..5;

dvar int U[Size] in 0..1;
dvar int+ S[Size];

//the constraints are:
sum(i in Size) U[ i ]*S[ i ]<=C;<br />
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#DecisionOptimization

Originally posted by: SystemAdmin

[akshayg said:]

If you are using Concert Technology, then you can do :-

IloModel model(env);
model.add(IloScalProd(U,S) <= C);<br />

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Originally posted by: SystemAdmin

[prubin said:]

Except that when you multiply two variables together in a constraint expression, the universe suffers sudden and irreversible heat death.  Or at least CPLEX will complain that the model's not linear.
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Originally posted by: SystemAdmin

[akshayg said:]

that's true, particularly because such a constraint is not Conic Quadratic representable (CQr) and CPLEX has no idea how to solve such models. Or maybe it is CQr ??
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